Optimal charging station locations and durations for a transit route with battery-electric buses: A two-stage stochastic programming approach with consideration of weather conditions

Abstract

While the environmental advantages of battery-electric buses (BEBs) are well-known, their significant differences from diesel buses require alterations to both route design (i.e., charging station locations) and operations (i.e., schedule management and holding control). The location, number, charging duration, and types of charging stations must be considered as part of the planning process. Charging stations can be located at depots, termini, or en-route. This paper considers the long-term planning and optimization problem of en-route charging station locations and charging duration to optimize passengers’ waiting time and operation and capital costs while addressing the weather-induced stochasticity of ridership and battery performance of the BEBs. A linear deterministic optimization model and a two-stage stochastic programming (SP) optimization process are developed to place BEB charging stations along the route and estimate their assigned charging time for both one-way and two-way operations. The developed approaches are tested on two high-demand bus routes in Calgary. The impact of the breakdown of the charging station associated with the maximum charging time on the schedule and the cost of the BEB operation is assessed. The solution of the stochastic model is analyzed using the expected value of perfect information as an index. The results indicate that using the SP model helps decrease the expected travel time of the route while the total cost per trip increases compared to the deterministic model.